Non contact method and apparatus for measurement of sheet resistance of P-N junctions

ABSTRACT

A contactless sheet resistance measurement apparatus and method for measuring the sheet resistance of upper layer of ultra shallow p-n junction is disclosed. The apparatus comprises alternating light source optically coupled with first transparent and conducting electrode brought close to the wafer, the second electrode placed outside of illumination area. Using the measurement of the surface photovoltage signals inside illuminated area and outside this area and its phase shifts, linear SPV model describing its lateral distribution the sheet resistance and p-n junction conductance is determined.

RELATED APPLICATIONS

U.S. application Ser. No. 12/319,755 Non-contact method and apparatusfor measurement of sheet resistance of P-N junction filed on Jan. 12,2009, is a division of U.S. application Ser. No. 10/688,766 filed onOct. 15, 2003, now U.S. Pat. No. 7,362,088.

BACKGROUND OF THE INVENTION

The present invention relates to the measurement of the sheet resistancein the upper layer of p-n junction.

Advances in semiconductor technology increase requirements to monitorepi and ion implant sheet resistance, Rs, in the range 50-5000ohms/square.

Currently 4-point probe technique is widely used for sheet resistancemeasurement. In the case of ultra shallow p-n junctions this techniquehas disadvantages: mechanical probes can poke through the implant layer;and probe pressures necessary for making ohmic contact with an implantlayer can create P-N junction leakage between the implant layer and theunderlying opposite conductivity substrate.

For these reasons, the 4-point probe techniques are inadequate for therequirements of ultra shallow P-N junction monitoring needs.

Non-contact surface photovoltage (SPV) technique can be used formeasurement of the sheet resistance. SPV is the change of the nearsurface bad bending or surface barrier under intensity modulatedillumination. As usually SPV is picked up by transparent and conductingelectrode brought near wafer surface illuminated area and used formeasurement of the minority carrier diffusion length, near surfacelifetime and doping level. In the case of strong inversion (for exampleif top surface of oxidized wafer p-type conductivity is charged withpositive ions) SPV can propagate outside of illuminating area due tolateral diffusion and the drift of the electrons and holes [V. N.Ovsyuk. Lateral diffusion of the minority carriers in thin semiconductorfilms, Sov. Phys. Semicond., v.16, p. 2146 (1982)].

The theory and experimental evidence of SPV propagation outside theillumination area in the silicon wafers with strong inversion surfacecondition was published in V. Faifer et. al. Measurement of thediffusion length with improved spatial resolution, Proceedings of24^(th) ESSDERC '94, Edinburgh, p. 601 (1994). The propagating of SPVoutside the illumination area strongly depends on the sheet resistanceof inversion layer or upper layer of p-n junction. The SPV equationdescribed in this paper can be used also for calculation of SPV spatialdistribution as function of coordinate x, y, light modulating frequency,sheet resistance and conductance in the case of silicon wafers in stronginversion or ultra shallow p-n junctions.

The non contact SPV technique for measurement of sheet resistance inultra shallow p-n junctions was proposed in US patent to Roger L.Verkuil, U.S. Pat. No. 5,442,297 in 1995. This technique is based on themeasurement of surface photovoltage (SPV) signals outside a localillumination area. To detect the attenuation and phase monitoring theapparatus include two conducting rings placed in the vicinity of thewafer surface outside the illumination area. Using the measurement oftwo AC SPV signals outside the illumination region and junctioncapacitance data the sheet resistance can be calculated.

This technique has follows disadvantages: since only attenuated SPVsignals are measured outside the illumination area this approach can notprovide good enough spatial resolution and high sensitivity formeasurements of sheet resistance Rs<400 Ohms/square in ultra shallow P-Njunction with high dose of implant. The measurement is based on smallsignal linear SPV theory. According to this theory SPV signal should belinear versus light flux not only outside illumination area but alsoinside this area. The technique presented in U.S. Pat. No. 5,442,297uses measurement only outside illumination area. The calculation ofsheet resistance is based on simplified model valid only for infinitelythin metal rings electrodes. As a result this model will give additionalsystematic error since capacitance of these thin electrodes shoulddepends non linear on its distance from the wafer surface and linearitycondition does not checked within illumination area. This probeconfiguration does not allow produce accurate measurement close to theedge of the wafer.

The advantages of present invention are to provide a method andapparatus for accurate measurements of sheet resistance of ‘less than400 Ohms/square with improved spatial resolution and sensitivity.

SUMMARY OF THE INVENTION

An object of this invention is to provide a non-contact sheet resistanceapparatus for measurement for low medium and high dose implant layers.The present embodiment of the invention apparatus includes means forillumination area of semiconductor structure, a transparent andconducting electrode installed near the surface of the semiconductorwafer directing light onto its surface and detecting SPV signal fromsaid area. The present invention also includes a second electrodedetecting SPV signals outside the illumination area. The secondelectrode can be a metal ring coaxial with transparent and conductingdisk of the first electrode. The second electrode can be a metal arc,which installed to be under the wafer, even if the light spot andtransparent electrode are located at the edge of the wafer. Using thisconfiguration of the second electrode, the edge effect can besignificantly decreased.

Another object of the invention is to provide a method for measurementof sheet resistance. To obtain accurate measurements, the intensity ofthe light is adjusted to obtain the linear dependence of SPV signal fromtransparent electrode versus light flux.

The first method uses measurement of the SPV signal only from the firstelectrode. This method requires the calibration using the wafer withknown sheet resistance. The method is based on comparison of SPV signalfor wafer with unknown sheet resistance and calibration wafer with Rsmeasured using 4-point probe. This calibration wafer should have thickenough upper layer of p-n junction to get accurate 4 point probemeasurement. The procedure of measurement includes the following steps:

-   -   a) Illumination the area of the semiconductor structure with        known sheet resistance through transparent electrode with        intensity modulated light;    -   b) Measurement of the SPV signal from transparent electrode;    -   c) Adjustment of the light flux to get linear dependence of the        SPV signal versus light flux;    -   d) Measurement of SPV signals Vs0;    -   e) Measurement of SPV signal Vs1 at the same conditions for        wafer with unknown Rs;    -   f) Determination of the sheet resistance using measured        RATIO=Vs1/Vs0, and the calculated curve or table RATIO (Rs).

The second method uses measurement of the SPV signals from the firstelectrode and second electrodes and provides the measurement of thesheet resistance without calibration sample. The procedure ofmeasurement includes the following steps:

-   -   a) Illumination the area of the semiconductor structure through        transparent first electrode with intensity modulated light at        maximum frequency, Fmax, corresponding bandwidth of SPV        preamplifier and lock-n amplifier;    -   b) Measurement of the SPV signal, Vs1, from transparent        electrode;    -   c) Adjustment of the light flux to get linear dependence of the        SPV signal, Vs1, versus light flux;    -   d) Measurement of SPV signals, Vs1 and Vs2 from the transparent        and not transparent electrodes;    -   e) If Vs1/Vs2>5 decreasing light modulating frequency to get the        ratio of SPV signals RATIO=Vs1/Vs2<5 and measurement of Vs1 and        Vs2 at this frequency;    -   g) Determination of the sheet resistance using measured        RATIO=Vs1/Vs2, and the calculated curve or table RATIO (Rs).

The third method uses measurement of the SPV signals and phase shiftsfrom the first and second electrodes and provides the measurement of thesheet resistance and conductance of p-n junction. The procedure ofmeasurement includes the following steps:

-   -   a) Illumination the area of the semiconductor structure through        transparent first electrode with intensity modulated light at        maximum frequency, Fmax, corresponding bandwidth of the SPV        preamplifier and lock-in amplifier;    -   b) Measurement of the SPV signal, Vs1, from transparent        electrode;    -   c) Adjustment of the light flux to get linear dependence of the        SPV signal, Vs1, versus light flux;    -   d) Measurement of SPV signals and its phase shifts, Vs1, Θ1 and        Vs2, Θ2 from first transparent and second non transparent        electrodes;    -   e) If Vs1/Vs2>5 decreasing the light modulating frequency to get        the ratio of SPV signals RATIO=Vs1/Vs2<5 and measurement of Vs1,        Θ1 and Vs2, Θ2 at this frequency;    -   f) Determination of the sheet resistance Rs and junction        conductance Gs using measured SPV signals and its phase shifts,        Vs1, Θ1 and Vs2, Θ2.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pictorial view of the present embodiment of the invention.

FIG. 2 is a pictorial view of a first SPV probe configuration.

FIG. 3 is a pictorial view of a second SPV probe configuration.

FIG. 4 is a pictorial view of the configuration of SPV electrodes withrespect to the wafer.

FIG. 5 is a pictorial view of the calculated dependence of the ratio ofSPV signal from first electrode versus sheet resistance normalized onSPV signal for p-n junction with sheet resistance Rs=400 Ohms/square.

FIG. 6 is a pictorial view of the calculated dependence of the ratio ofSPV signals from first and second electrodes versus sheet resistance.

DETAILED DESCRIPTION OF THE APPARATUS AND METHOD

In FIG. 1, a contactless sheet resistance measurement apparatus 1 isshown. Wafer 2 is placed on a wafer chuck 3. The wafer chuck is placedon the rotary stage 4. The rotary stage 4 is installed on the linearstage 5. The apparatus comprises an SPV probe 6, which is placed closeto the wafer surface and optically coupled through fiber bundle 8 withthe LED 7, connected to the LED driver 9. Two electrical outputs of theSPV probe 6 are connected to the lock-n amplifiers 10 and 11. Lock-inamplifiers 10 and 11, step motors of stages 4 and 5 are electricallyconnected to interface and computer 12.

SPV probe 6 represented at FIG. 2 includes dielectric ring 13, a glassdisk with transparent and conducting ITO coating 14, two metalelectrodes like the rings 15 and 16. Conducting layer of glass disk 14is connected to preamplifier 17, metal electrode 15 is grounded andmetal electrode 16 is connected to the preamplifier 18. The output ofpreamplifier 17 is connected to the lock-in amplifier 10 and output ofpreamplifier 18 is connected to the lock-in amplifier 11.

SPV probe 6 represented at FIG. 3 includes dielectric ring 13, a glassdisk with transparent and conducting ITO coating 14, two metalelectrodes like the part of the ring 15 and 16. Conducting layer ofglass disk 14 is connected to preamplifier 17, metal electrode 15 isgrounded and metal electrode 16 is connected to the preamplifier 18. Theoutput of preamplifier 17 is connected to the lock-in amplifier 10 andoutput of preamplifier 18 is connected to the lock-in amplifier 11. Asshown at FIG. 4 the SPV probe is installed to provide the electrodes 15and 17 inside the wafer, when transparent electrode 14 is close to theedge of the wafer.

The method of measurement is based on the solution of the equation forSPV value as function of coordinate x,y, derived in publication theProceedings of 24^(th) ESSDERC '94, Edinburgh, p. 601 (1994). After somemodification the equation can be written as:

$\begin{matrix}{{\frac{\partial^{2}v_{SPV}}{\partial x^{2}} + \frac{\partial^{2}v_{SPV}}{\partial y^{2}}} = {{{Rs} \cdot {Cs} \cdot \frac{\partial v_{SPV}}{\partial t}} + {{Rs} \cdot G \cdot v_{SPV}} - {q \cdot \varphi \cdot \left( {1 - R} \right) \cdot {Rs}}}} & (1)\end{matrix}$where:

ν_(SPV)(x,y,t) is SPV value as function of coordinates x,y;

φ(x,y,t) is the intensity of light flux;

Rs is the sheet resistance of the upper layer of p-n structure;

Cs is the capacitance of p-n junction per unit area;

G is the conductivity of p-n junction per unit area;

R is reflectivity of semiconductor.

The conductivity of p-n junction can be determined as:

$\begin{matrix}{G = \frac{I_{0} \cdot q}{k \cdot T}} & (2)\end{matrix}$where

q is charge of the electron;

k is Boltzman constant;

T is the temperature;

Io is the prefactor in formula of current, I, versus voltage, V, of p-njunction:I=I₀·[exp(q·V/kT)−1]  (3)

The capacitance of the p-n junction can be calculated using formula:

$\begin{matrix}{{Cs} = {\frac{\sqrt{ɛ_{SI}ɛ_{0}q^{2}N}}{2\;{kT}}/\sqrt{{2{\ln\left( \frac{N}{ni} \right)}} + {\ln\left( {\ln\left( \frac{N}{ni} \right)} \right)}}}} & (4)\end{matrix}$where:

ε₀ is the permittivity of vacuum;

ε_(SI) is the permittivity of silicon;

q is the magnitude of electronic charge;

kT is the thermal energy;

ni is the intrinsic concentration of charge carriers in semiconductor;and

N is concentration of the majority carriers in semiconductor substrate.

The SPV signal can be calculated using the formula:

$\begin{matrix}{{V_{SPV}(t)} = {{Const}{\int_{S}^{\;}{\int{{v_{SPV}\left( {x,y,t} \right)}{\mathbb{d}x}\ {\mathbb{d}y}}}}}} & (5)\end{matrix}$where S is the area of electrode, Const is the value, which depends onthe air gap between electrode and the semiconductor surface, the gain ofamplification of the preamplifier and others parameters.

In the case of sinusoid modulated light SPV signal can be representedas:V_(SPV)(t)=V_(S)·exp(jω·t)=|Vs|exp(jθ)exp(jωt)  (6)where |Vs|,

are the magnitude and phase shift of SPV signal, Vs, ω=2πF, F is lightmodulating frequency.

Using the equation (1), formula (5) we can get the formulas for SPVsignals from electrodes installed inside, Vs1, and outside, Vs2, theillumination area:

$\begin{matrix}{V_{S\; 1} = {\frac{q\;\Phi\; R_{S}}{k^{2}}\left\lbrack {1 - {\frac{2}{{kR}_{0}}\frac{{I_{1}\left( {kR}_{0} \right)}{K_{1}\left( {kR}_{0} \right)}}{{{I_{0}\left( {kR}_{0} \right)}{K_{1}\left( {kR}_{0} \right)}} + {{I_{1}\left( {kR}_{0} \right)}{K_{0}\left( {kR}_{0} \right)}}}}} \right\rbrack}} & (7) \\{V_{S\; 2} = {2\; q\frac{\Phi\; R_{S}}{k^{3}R_{0}^{2}}\frac{{I_{1}\left( {kR}_{0} \right)}\left\lbrack {{R_{1}{K_{1}\left( {kR}_{1} \right)}} - {R_{2}{K_{1}\left( {kR}_{2} \right)}}} \right\rbrack}{{{I_{0}\left( {kR}_{0} \right)}{K_{1}\left( {kR}_{0} \right)}} + {{I_{1}\left( {kR}_{0} \right)}{K_{0}\left( {kR}_{0} \right)}}}}} & (8)\end{matrix}$wherek=√{square root over (RsG+jωRsCs)}  (9)

I₀(z), I₁(z), are the modified Bessel function of the first kind;

K₀(z), K₁(z) are the modified Bessel function of the second kind;

R₀ is the radius of the first transparent electrode;

R₁, R₂ are the inner and outer radiuses of the second non transparentelectrode;

Φis the effective light flux propagating inside semiconductor.

If light modulating frequency is high enough, ω>>G/Cs, SPV signal doesnot depend on leakage of p-n junction and sheet resistance can becalculated using measured values of the magnitudes of SPV signals fromfirst transparent electrode, Vs1, and second non transparent electrodeand equation:

$\begin{matrix}{\frac{{Vs}\; 1}{{Vs}\; 2} = {{\frac{V_{S\; 1}}{V_{S\; 2}}} = {{\frac{1}{2}{kR}_{0}^{2}\frac{{{K_{1}\left( {kR}_{0} \right)}{I_{0}\left( {kR}_{0} \right)}} + {{K_{0}\left( {kR}_{0} \right)}{I_{1}\left( {kR}_{0} \right)}} - {\left( {{1/2}{kR}_{0}} \right){K_{1}\left( {kR}_{0} \right)}{I_{1}\left( {kR}_{0} \right)}}}{{I_{1}\left( {kR}_{0} \right)}\left\lbrack {{R_{1} \cdot {K_{1}\left( {kR}_{1} \right)}} - {R_{2}{K_{1}\left( {kR}_{2} \right)}}} \right\rbrack}}}}} & (10)\end{matrix}$where Cs is calculated using formula (5);k=√{square root over (j2πFRsCs)}

For leaky p-n junctions and low frequency, F, sheet resistance andconductance can be calculated using the measured magnitudes and phaseshifts of SPV signals Vs1,θ1 and Vs2,θ2, and a set of equations:

$\begin{matrix}{\frac{{Vs}\; 1}{{Vs}\; 2} = {{\frac{V_{S\; 1}}{V_{S\; 2}}} = {{\frac{1}{2}{kR}_{0}^{2}\frac{{{K_{1}\left( {kR}_{0} \right)}{I_{0}\left( {kR}_{0} \right)}} + {{K_{0}\left( {kR}_{0} \right)}{I_{1}\left( {kR}_{0} \right)}} - {\left( {{1/2}{kR}_{0}} \right){K_{1}\left( {kR}_{0} \right)}{I_{1}\left( {kR}_{0} \right)}}}{{I_{1}\left( {kR}_{0} \right)}\left\lbrack {{R_{1} \cdot {K_{1}\left( {kR}_{1} \right)}} - {R_{2}{K_{1}\left( {kR}_{2} \right)}}} \right\rbrack}}}}} & (11) \\{{\theta_{1} - \theta_{2}} = {{Arg}\left\lbrack {\frac{1}{2}{kR}_{0}^{2}\frac{{{K_{1}\left( {kR}_{0} \right)}{I_{0}\left( {kR}_{0} \right)}} + {{K_{0}\left( {kR}_{0} \right)}{I_{1}\left( {kR}_{0} \right)}} - {\left( {{1/2}{kR}_{0}} \right){K_{1}\left( {kR}_{0} \right)}{I_{1}\left( {kR}_{0} \right)}}}{{I_{1}\left( {kR}_{0} \right)}\left\lbrack {{R_{1} \cdot {K_{1}\left( {kR}_{1} \right)}} - {R_{2}{K_{1}\left( {kR}_{2} \right)}}} \right\rbrack}} \right\rbrack}} & (12)\end{matrix}$

The results of calculation using formula (7) SPV signal from transparentelectrode versus sheet resistance for light modulating frequency f=100kHz and the diameter of transparent electrode 5 mm is represented atFIG. 5. This curve is normalized on SPV signal for p-n junction withsheet resistance Rs=400 Ohms/square. The substrate doping concentrationis 10¹⁵ cm³.

FIG. 6 shows the calculated using formula (10) dependence of the ratioof SPV signals, Vs1/Vs2, from first and second electrodes versus sheetresistance for light modulating frequency f=100 kHz, diameter of thetransparent electrode is 5 mm, the inner and outer diameters of themetal ring electrode are 16 and 18 mm. The substrate dopingconcentration is 10¹⁵ cm⁻³.

The first method uses measurement of the SPV signal from the firstelectrode. This method requires the calibration using the wafer withknown sheet resistance. The method is based on comparison of SPV signalfor wafers with unknown sheet resistance and calibration wafer with Rsmeasured using 4-point probe. This calibration wafer should have thickenough upper layer of p-n junction to get accurate 4 point probemeasurement

The procedure of measurement includes the following steps:

-   -   a) Illumination the area of the semiconductor structure with        known sheet resistance through transparent disk 14 with        intensity modulated light at frequency, f, from LED 17;    -   b) Measurement of the SPV signals Vs0 from transparent electrode        14;    -   c) Adjustment of the light flux to get linear dependence of the        SPV signal Vs0 versus light flux;    -   d) Measurement of SPV signal Vs0; Measurement of SPV signal Vs1        at the same conditions for wafer with unknown Rs;    -   e) Determination of the sheet resistance using measured        RATIO=Vs1/Vs0, and equation (7).

The second method uses measurement of the SPV signal from the first andsecond electrodes. The procedure of measurement includes the followingsteps:

-   -   a) Illumination the area of the semiconductor structure through        transparent disk 14 from LED 17 with intensity modulated light        at frequency, Fmax, corresponding to bandwidth of SPV        preamplifier and lock-n amplifier;    -   b) Measurement of the SPV signal, Vs1, from transparent        electrode;    -   c) Adjustment of the light flux to get linear dependence of the        SPV signal, Vs1, versus light flux;    -   d) Measurement of SPV signals, Vs1 and Vs2 from electrodes 14        and 16 respectively using preamplifiers 17 and 18;    -   e) If Vs1/Vs2>5 decreasing of light modulating frequency to get        the ratio of SPV signals RATIO=Vs1/Vs2<5 and measurement of SPV        signals at this modulating frequency;    -   f) Determination of the sheet resistance using measured        RATIO=Vs1/Vs2, and equation (10).

For leaky p-n junctions condition ω>>Gs/Cs can not be valid even forhigh frequency F>10 kHz. In this case the additional measurement of theSPV phase shift should be provided and Rs, Gs can be calculated usingset of equations (11), (12), where Vs1, Vs2 and Θ1,Θ2 are the measuredmagnitudes and phase shifts of SPV signals from first transparent andsecond non transparent electrodes.

The third method uses measurement of the SPV signals and phase shiftsfrom the first and second electrodes. The procedure of measurementincludes the following steps:

-   -   a) Illumination the area of the semiconductor structure through        transparent disk 14 from LED 17 with intensity modulated light        at frequency, Fmax, corresponding the bandwidth of SPV        preamplifier and lock-in amplifier;    -   b) Measurement of the SPV signal, Vs1, from transparent        electrode;    -   c) Adjustment of the light flux to get linear dependence of the        SPV signal, Vs1, versus light flux;    -   d) Measurement of SPV signals and its phase shifts, Vs1, Θ1 and        Vs2, Θ2 from electrodes 14 and 16 respectively using        preamplifiers 17 and 18;    -   e) If Vs1/Vs2>5 decreasing the light modulating frequency to get        the ratio of SPV signals RATIO=Vs1/Vs2<5 and measurement Vs1 and        Vs2 at this modulating frequency;    -   f) Determination of the sheet resistance Rs and junction        conductance Gs using measured SPV signals and its phase shifts,        Vs1, Θ1 and Vs2, Θ2 and set of equation (6) and (7).

1. A contactless sheet resistance measurement method, comprising thesteps of: illumination the area of the semiconductor structure through atransparent electrode with intensity modulated light at maximumfrequency corresponding to bandwidth of SPV preamplifier and lock-inamplifier; measurement of the SPV signal, Vs1, from the transparentelectrode; adjustment of the light flux to get linear dependence of theSPV signal, Vs1, versus light flux; measurement of SPV signals, Vs1 andVs2; adjustment of light modulating frequency to get the ratio of SPVsignals RATIO=Vs1/Vs2<5 and measurement of Vs1 and Vs2 at thisfrequency; and determination of the sheet resistance using measuredRATIO=Vs1/Vs2, and the calculated curve or table RATIO(Rs).